Understanding Efficiency Ratios
Let the efficiency of B be represented by $E_B$.
- The efficiency of A ($E_A$) is $40\%$ of B's efficiency: $E_A = 0.40 \times E_B = 0.4 E_B$
- The combined efficiency of A and B is: $E_A + E_B = 0.4 E_B + E_B = 1.4 E_B$
- The efficiency of C ($E_C$) is $50\%$ of the combined efficiency of A and B: $E_C = 0.50 \times (E_A + E_B) = 0.5 \times (1.4 E_B) = 0.7 E_B$
Calculating Total Work and Combined Efficiency
Let the total work required to complete the task be $W$. The formula relating work, efficiency, and time is $W = \text{Efficiency} \times \text{Time}$.
- We know C completes the task alone in $30$ days. Using C's efficiency: $W = E_C \times 30 \text{ days}$ $W = (0.7 E_B) \times 30 = 21 E_B$
- Now, let's find the combined efficiency of A, B, and C working together: $E_{A+B+C} = E_A + E_B + E_C$ $E_{A+B+C} = 0.4 E_B + E_B + 0.7 E_B = 2.1 E_B$
Determining Time for Combined Effort
We need to find the time ($T$) it takes for A, B, and C together to complete the work $W$.
- Using the formula $W = E_{A+B+C} \times T$: $21 E_B = (2.1 E_B) \times T$
- Solve for $T$: $T = \frac{21 E_B}{2.1 E_B}$ $T = \frac{21}{2.1} = 10$
Therefore, A, B, and C together can complete the task in $10$ days.
Similar Questions
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- Anjani can do a certain piece of work in 24 days. Anjani and Khushbu can together do the same work in 12 days, and Anjani, Khushbu and Sushmita can do the same work together in 9 days. In how many days can Anjani and Sushmita do the same work together?
- Hema can do a certain piece of work in 30 days. Hema and Raji can together do the same work in 22 days, and Hema, Raji and Smitha can do the same work together in 15 days. In how many days can Hema and Smitha do the same work together?
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- Working $5\text{ h}$ a day, A can complete a task in $8\text{ days}$ and working $6\text{ h}$ a day, B can complete the same task in $10\text{ days}$. Working $8\text{ h}$ a day, they can jointly complete the task in:
- A does half as much work as B in three-fourth of the time taken by B. If together they take $12\text{ days}$ to complete the work, how much time shall B take to do it alone?
- A can complete a piece of work in 60 days. He worked for 15 days and B finished the remaining work in 30 days. If they work together then the work will be completed in:
- If 24 persons can complete a task in 5 days, in how many days, 6 persons would be able to complete it?
- 15 men or 25 women can reap a field in 22 days. How many days will 9 men and 18 women take to reap it?
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Important Questions from Time and Work
A and B can do a piece of work in 18 days. B and C together can do it in 30 days. If A is twice as good a workman as C, find in how many days B alone can do the work?
Two men and 7 women can complete a work in 28 days, whereas 6 men and 16 women can do the same work in 11 days. In how many days will 5 men and 4 women, working together, complete the same work?
A man and a woman, working together can do a work in 66 days. The ratio of their working efficiencies is 3 ∶ 2. In how many days 6 men and 2 women together can do the same work?
Each one of five men independently can complete a work in 20 days. The work is started by one person. Next day one more person joins and every next day one more person joins. From the fifth day, five persons continued working as a team. In how many days, will the work be completed?
Numan does half the work as Gagan in 4/5 of the time. If together they take 16 days to complete a piece of work, then how long will it take Gagan to complete the work?
